Download Encoding Information in Neuronal Activity

Encoding Information
in Neuronal Activity
Michael Recce
4.1 Introduction
Neurons communicate by producing sequencesof fixed size electrical impulses
called action potentials or spikes. Perceptions, decisions, and ideas
are all encoded into trains of action potentials , but the basis of this coding
schemeis still not well understood . Deciphering this code is one of the primary
goals in experimental neuroscience. This chapter presents some of
the data on the firing properties of neurons, along with Clueson the coding
schemesthat have emerged from this data.
As described in Chapter 1, it is widely believed that neurons use firing
rate to signal the strength or significance of a response. This hypothesis
was first proposed by [Adrian, 1926] from the study of the relationship
between the activity pattern of a stretch receptor in frog muscle and the
amount of weight applied to the muscle. Figure 4.1 shows some of the
data that Adrian used to develop the firing rate code hypothesis . This
nerve fiber has what is now considered a classic response function . The
firing rate monotonically increaseswith an increase in the strength of the
stimulus . The initial part of the response function is approximately linear
and it saturates at the maximum firing rate of the neuron, which generally
ranges from 100 to 500 spikes per second.
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4. EncodingInformationin NeuronalActivity
Adrian also discovered that neurons only transiently sustain a high firing
rate. In the presenceof a persistent stimulus the firing rate gradually decreases
[Adrian, 1926, Adrian , 1928] .
This transient elevated firing is found in the majority of cells in the
visual cortices [Hubel and Wiesel, 1962, Maunsell and Gibson, 1992],
cortex
cortex
[Mount castle, 1957] ,
auditory
somatosensory
[Brugge and Merzenich, 1973] and many other brain regions. Adrian
as an adaptation to the stimulus and his hypothesis
interpreted this decrease
was that the animal ' s perceived level of sensation was directly reflected
by the instantaneous firing rate, as shown in Figure 4.2.
Sti
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proposedby Adrian
Figure4.2. Relationship
(1928
). If boththe receptorandthe organismhabituateto a persistentstimulus
in firingratemightexactly
with thesametimescalethentheposttransientdecrease
.
of thestimulus.RedrawnfromAdrian, 1928
reflectthedegreeof sensation
The instantaneous firing rate of a neuron is considered to be a direct measure
'
of the extent to which a recent stimulus matches the neuron s ideal
stimulus .
Numerous studies in sensory and motor systems of a wide range of species
have supported the validity of the firing rate code hypothesis . For example
, pressure receptor cells in the skin appear to use a frequency code to
signal the intensity of the stimulus . The contraction of a muscle is roughly
proportional to the firing rate of the motor neuron that enervates the muscle
. A subset of the output cells from the retina fire at a maximum rate
when there is a bright circle of light surround by a dark angular ring illuminating
a specific spot on the retina. The ideal stimulus pattern is also
the
called
receptive field of the cell.
The successof the firing rate code hypothesis has led to a method in neuroscience
111which the role of neurons is established by searching for the
4.1 Introduction
113
stimulus that elicits the largest firing rate from a cell [Lettvin et al., 1959] .
In fact the firing rate code hypothesis has led to the discovery of the role
of neurons that are further from sensory receptors or muscles. Hubel and
Wiesel used the firing rate hypothesis to discover that some of the neurons
in the primary visual cortex are edge detectors [Hubel and Wiesel, 1959,
Hubel and Wiesel, 1962] .
Placecells in a brain region called the hippo campus, which is anatomically
far from the sensory and motor systems, were given this name because
they fire maximally when an animal is in a particular place in a particular
environment [O' Keefe and Dostrovsky, 1971] . Neurons in the temporal
lobes of primates have also been found fire maximally in response to particular
objects or for faces.
The properties of these and many other types of neurons in the central
nervous system were discovered by applying the firing rate hypothesis .
Strong physiological support for the firing rate hypothesis is also found in
the model of a neuron as a temporal integrator . As a temporal integrator ,
a neuron will lose the precise time of arrival of individual spikes. The
amount of postsynaptic depolarization will depend only on the number of
spikes arriving at the neuron and the process of synaptic transmission of
these spikes. Further, if the firing rate is a direct function of the level of
depolarization of the cell then the firing rate is a direct indication of the
internal state (or the degree to which the cell is excited).
Neurons act as temporal integrators if the time constant of integration is
long in comparison with the average time between spikes. In contrast if
the integration time constant is short, the neuron could also act as a coincidence
detector [Abeles, 1982, Konig et al., 1996], and therefore be sensitive
to the precise arrival time of the spikes for presynaptic neurons.
The hypothesis that the firing rate is proportional to the level of depolariza tion in cortical cells has been tested explicitly by injecting fixed amplitude
current pulses into the soma (e.g. [Mainen and Sejnowski, 1995]). While
the firing rate is shown to be a function of the level of depolarization in
these experiments, this fixed amplitude current results in a spike train in
which the intervals between spikes varies between stimulus presentations.
This type of variation in neuronal response to repeated identical stimuli is
sometimes interpreted as noise [Shadlen and Newsome, 1994] . The nature
of this apparent noise or jitter in neuronal activity is discussed in detail in
Section 4.6.
Rate coding also makes it easier to model the function of the neurons, since
the rate can be modeled by a single continuous variable. Essentially this
removes the need to describe explicitly the behavior of the individual neurons
in the system in the time domain . This simplification has been used
in the majoritY of current models of networks of neurons.
However , in recent years evidence has been accumulating that suggests
that firing rate alone cannot account for all of the encoding of information
in spike trains. Some of this data supports encoding schemes that are in
addition to firing rate, while other data describes changes in firing patterns
that code for stimuli in the absenceof changes in firing rate. Also ,
4. Encoding Information in Neuronal Activity
114
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4.2 Synchronization
andOc;cillatinn
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In one example the correlated firing between two neurons during the GO
tasks was highest during the first second after the onset of the stimulus
and lower during the next second. During the NO- GO tasks the pattern of
correlated firing was reversed. The correlation was low in the first second
and high in the following second. There was no difference in the firing
rates between the two paradigms and no difference in the cross-correlation .
These rapid changesin the correlation of activity were found in 32% of 947
pairs of recorded neurons.
Most neurons in the auditory cortex have a transient response to the onset
of a stimulus [Brugge and Merzenich , 1973] . In a recent experiment multiple
isolated singe neurons from several sites in the auditory cortex of anesthetized
marmoset monkeys were recorded from simultaneously, while the
animal was presented with a pure tone stimulus (4 kHz ) that is known to
drive these neurons [deCharms and Merzenich , 1996] .
The firing pattern, and the correlations between simultaneously recorded
neurons in two separated recording sites, were examined in a number of
different conditions , two of which are illustrated in Figure 4.3. In one of
these conditions there is a persistent tone, and in the other there is a short
(50 ms) tone. Cross correlations calculated during a 3 s period , 500 ms after
stimulus onset, in each of these two conditions were compared. In both
casesthere was a transient change in the firing rate, but only during the
persistent tone signal there was a zero phase shift synchronization between
the firing of the neurons. The significance of this effect was higher when
action potentials from several neurons recorded from the same site were
combined and correlated with several neurons in a second recording site,
suggesting that the correlated activity is a population phenomenon. This
data suggeststhat the temporal structure of the population activity , rather
than the firing rate of individual neurons, is used to encode the presence
of the tone.
In a recent study sets of neurons in the primary motor cortex (M1 ) of the
macaque monkey were found to synchronize when the animal was preparing
to respond to a stimulus [Riehle et al., 1997] . In each trial the animal
waited for one of four different delay periods (600, 900, 1200and 1500milliseconds
), prior to making a motor response. The ordering of the trials
was random so that the animal could not predict the length of a particular
delay period . In the data from the longest delay trials there was a significant
increase in the synchronized activity of pairs and triplets of neurons
at points in time corresponding to the shorter delays. This synchronized
activity was present without a change in the firing rate of the neurons. In
contrast, the motor and sensory components of the task were correlated
with changes in the firing rate of the neurons.
The synchro~ ed firing of sets of neurons, which is suggested to be more
correlated with internal , rather than external events can not be subsumed
within a model or description of neuronal function that only includes firing
rate. In all three examples discussed in this section firing rate did not indicate
a state change that was only apparent by examining the synchronized
activity of simultaneously recorded cells. The first example the synchronization
supported the idea that there was a perceptual grouping of stimu -
4. Encoding Information in Neuronal Activity
116
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Figure 4.3. Mean firing rate and temporal correlation of neurons recorded by
[de Charms and Merzenich, 1996] from the primary auditory cortex of a marmoset
monkey. Part e of the figure shows the envelope of a 4kHz pure tone stimulus , f
and g contain the mean firing rates of neurons simultaneously recorded from two
cortical locations, and parts a- d contain average cross-correlations computed from
100 stimulus presentations. In parts a-d the mean is shown with a thick line and
the mean plus standard error is shown with a thin line . Part a contains the cross
correlation during a silent period before the stimulus ; b is the correlation during a 3
second constant phase of a ramped onset pure tone; c is the 3 second period after a
sharp onset pure tone; and d is the correlation during a silent period after a short 50
ms pure tone. Reprinted with permission from [deCharms and Merzenich, 1996.]
Ius features [Milner , 1974, von der Malsburg, 1981] . In the second example
the synchronization coded for the presenceof a basic auditory feature, and
in the third example the synchronization signaled the presenceof an internal
state that would otherwise not be observed (seealso section 1.1.3.3).
4.3
Temporal Binding
Synchronized activity in populations of neurons in cortical
and subcortical regions, and in species as diverse as turtles
rats
[Prechtlet al., 1997
],
pigeons [Neuenschwanderet al., 1996],
al.
et
1995
cats
and
1989
and
,
,
,
[Bragin
]
[Gray
]
Singer
monkeys
[Livingstone, 1996, Kreiter and Singer, 1996] is often found to coincide
with oscillationsin the gammafrequencyrange (20-70 Hertz). This
synchronizationcan occur with zero phasedelay acrossmultiple visual
associationareas, betweenvisual and motor areas, and betweencortical
4.3 Temporal
Binding
117
and subcortical regions. The presenceof the zero phase shift synchronized
firing has been shown to exist between particular subsets of neurons
within an area and to occur in relation to specific behavioral events. In
the cat visual system synchronized activity was found in cells in separate
cerebral hemispheres [Engel et al., 1991] . The evidence for synchronized
activity and the significance of this phenomenon has been recently
thoroughly reviewed [Singer and Gray, 1995, Engel et al., 1997] .
It has been suggested that this synchrony provides a means to bind
together in time the features that represent a particular stimulus
[Milner , 1974, von der Malsburg, 1981, von der Malsburg, 1995] . There is
substantial evidence to suggest that the individual features of a perceived
object are encoded in distributed brain regions and fire collectively as a cell
assembly [Hebb, 1949] .
1
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sphere
red
cube
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Figure 4.4. Temporal binding of features in cell assemblies. In this example both
a red sphere and a blue cube are present in a scene. If sets of neurons code for
the colors red and blue , and the for the shapes sphere and cube, then the correct
association of color and shape might be represented in the brain by synchronizing
the activity of the the neurons within each of the two cell assemblies. In this way
neurons coding for red and sphere are active at a different time from those coding
for blue and cube, and the two objects can be processedsimultaneously .
The central idea is that there is some temporal process during which information
about an object or group of objects is processed. In order to keep the
attributes of these objects from interfering, they are separated in time , as illustrated
in Figure 4.4. In this figure there are two cell assemblies, one that
codes for the features of a red sphere and one that codes for the features
of a blue cube. Within a cell assembly the neurons fire in a synchronized
pattern with zero phase shift . There is a time shift between the two assemblies
so that each remains coherent, and the sceneis not confused with
one containing a blue sphere and a red cube. With firing rate coding it is
not possible to construct this type of neuronal system in which multiple ,
simultaneous use is made of a set of feature encoding neurons.
118
4. Encoding Information in Neuronal Activity
4.4 Phase Coding
During locomotion, the firing patterns of neurons in the rat hippo campus
are modulated by a large 7- 12 Hz sinusoidal oscillation called the theta
rhythm . The theta rhythm is generated in the hippo campus [Green et al.,
1960] from a pacemaker input located in the medial septum [Petsche et
al., 1962] . It is highly coherent, with no phase shift over a large region of
the hippo campus called CA1 [Bullock et al., 1990] . Many neurons in the
CA1 and neighboring CA3 region of the hippo campus have acharacteristic
burst firing pattern pattern [Ranck, 1973, Fox and Ranck, 1975], and
the activity pattern of the majority of these neurons, called place cells, is
highly correlated with the animals location in an environment [O' Keefe
and Dostrovsky, 1971] .
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Figure4.5. Extractionof the firing phasefor eachspikeduring a singlerun through
the placefield of a placecell on the linear runway. (A ) Eachactionpotentialfrom
cell 3 during the one secondof data shownin the figure is markedwith a vertical
line. (B) The phaseof eachspike relative to the hippocampaltheta rhythm. (C)
Hippocampaltheta activity recordedat the sametime as the hippocampalunit.
( D) Half sine wave fit to the theta rhythm which was usedto find the beginning
of eachthetacycle(shown with vertical ticks aboveand below the thetarhythm).
, 1993].
Reprintedfrom [O' Keefeand Recce
4.5 Dynamic Range and Firing Rate Codes
119
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Figure 4.6. Phaseof EEG at which a hippocampalplace cell fired, (A ) plotted
againstthe position of the rat and (C) againstthe time after the rat crossedthe
nearestboundary of the placefield. (8) and ( D) show the distribution of the firing
rate recordedin the 41 runs along the runway that were usedto constructthe
, 1993].
figure. Reprintedfrom [O' Keefeand Recce
In addition the phase relationship between the place cell activity and the
theta rhythm was found to have a higher level of correlation with the animals
spatial location than with the time that the animal has spent in the
field
[O' Keefe and Recce, 1993] . Figure 4.6 illustrates this phenomena
place
. In panel A , the phase of each spike from a place cell is plotted against
the position of the animal , recorded on multiple runs along the runway .
Panel B shows that the firing rate of the place cell is highest in the center of
the place field . In panel C and panel D the same data are plotted as a function
of the time that has passedsince the animal entered the place field . The
phase of the firing of this cell and 14 other place cells had a higher correlation
to the spatial location, and the phase of firing was a better indication
of the animal' s location than the firing rate of the cell.
The phase of place cell firing provides additional information on the animal ' s spatial location which is independent of and more informative than a
firing rate code. One possibility is that these different types of information
are intended for different target regions in the brain . Also phase coding,
like temporal binding, provides a way for the information on neighboring
spatial locations to be processedsimultaneously without interference (see
also Section 1.i .3.2).
4.5
Dynamic Range and Firing Rate Codes
Forover forty yearsit hasbeenknown that a firing ratecodeis not the most
efficient way for a neuron to transmit information with action potentials
120
4. Encoding l.nform ;ltion in Neuronal Activity
[MacKay and McCulloch , 1952] . As a simplified illustration consider the
the output signal from a neuron that has a firing rate scalethat ranges from
zero to 200 spikes per second. With the further assumptions that: (1) the
critical time interval for integrating the signal or measuring the firing rate
is 100 ms, and (2) that there is uncertainty in the generation of spikes, the
hypothetical neuron has approximately 20 distinct states.
In contrast if information is coded in the length of inter -spike intervals
with five millisecond precision then there are over a million possible output
states (22 ), although not all of these states would be equally probable .
There are a wide range of possible codes that have more than 20 and less
than a million different states in a 100 millisecond interval . In particular
the coding scheme might look largely like a firing rate, but contain additional
information that is only extracted by a subset of the neurons that
receive inputs from a particular neuron.
One hundred milliseconds might also be an overestimate of the length of
the time interval used to transmit the coded signal . A housefly can change
its flight path in reaction to a change in visual input in just 30 milliseconds
[Land and Collett , 1974] . In a recent study Thorpe and coworkers
showed that the total time required for human subjects to perform a pattern
recognition task was 150 milliseconds [Thorpe et al., 1996] . Since this
task is thought to require many synaptic steps and substantial signal propagation
delays, it appears that the information sampling interval taken by
each neuron must be much less than 100 milliseconds .
Some of the most convincing evidence that precise timing of spikes provides
additional information , not present in firing rate alone has come
from experiments carried out by van Steveninch , Bialek and coworkers.
The timing sequenceof action potentials in the HI neuron of the fly have
been shown to contain the information needed to reconstruct the stimulus
pattern . This reconstruction implies that there is a precision on the order of
a millisecond in the firing of each spike. Furthermore they have shown that
the HI neuron only produces one or two spikes in the 30 milliseconds that
a fly samples before it can make a response, suggesting that the information
encoded in the interspike intervals must be used by the downstream
neurons. These data and analysis are presented in great detail in a recent
book [Rieke et al., 1997] .
4.6 Interspike Interval Variability
All of the proceeding discussion in this chapter has neglected the presence
of temporal noise or jitter in the firing patterns of neurons . Temporal
noise obviously reduces the number of distinguishable states of
an individual neuron , independent of the coding scheme that is being
used . Softky and Koch examined the variability in the interspike intervals
recorded from cortical cells [Softky and Koch , 1993] , that were firing
at an average constant rate and found that the intervals between spikes
were randomly distributed . They considered this irregularity as evidence
that the neurons were acting as coincidence detectors , and that the vari ability was part of the signal rather than noise . However , it has been argued
[Shadlen and Newsome , 1994] that this data supported the hypoth -
4.6 Interspike Interval Variability
121
esis that neurons were undergoing an internal random walk that results
from a roughly equal amount of inhibitory and excitatory input .
An explanation has been found for some of the measured firing irregularity
in cortical neurons. Variability found in the interspike intervals of
neurons in the visual cortex in anesthetized animals is in part due to the
influence of intracortical and thalamocortical oscillations that are a direct
result of the anesthesia [Arieli et al., 1996] . This noise can be reduced by
using awake animals and by controlling for the noise introduced by small
eye movements [Gur et al., 1997] .
Some of the hypothesized noise in individual neurons might be removed
by combining firing rate information accumulated from a population
of neurons. Georgopoulos and coworkers have shown that in
the motor cortex a population of neurons provides a better correlation
to the motor activity than individual cells [Georgopoulos et al., 1986]
[Wilson and Mc Naught on, 1993] have shown one way in which the firing
rate of a population of hippocampal place cells could be combined to provide
a better estimate of a rat' s location .
In general there are two ways in which a population of neurons can improve
the accuracy of the encoding of a stimulus or motor output . Each
neuron could have a coarse coding of the stimulus , which is made finer
by the activity of a number of neurons. Alternatively each neuron could
have independent noise, and this noise is removed by combining input
from several neurons. In the two examples discussed here the combined
population activity is more precise or informative becauseeach neuron is
providing additional information , rather than independent noise (see also
Section 1.1.2. 3).
H the interspike interval irregularity is noise it can only be removed if this
noise is independent in the set of neurons whose activity is averaged. In
a recent experiment Shoham and coworkers used voltage sensitive dyes
to measure the extent to which neighboring neurons in the visual cortex
have independent uncorrelated activity patterns [Shoham et al., 1997] . The
activity patterns of neighboring regions of cortex were highly correlated,
suggesting that a downstream neuron receives multiple projections with
similar interspike intervals , and does not average out the variations . PrectIe and coworkers found similar results is the visual cortex of the turtle
[Prechtl et al., 1997] . A wave pattern is generated as a result of the presentation
of a stimulus , which changeswith each presentation of the stimulus
but is correlated between neighboring regions of the cortex, within the presentation
of the stimulus .
In one recent study, the amount of information and noise in spike trains
was quantified . The results from this experiment show that the amount of
variation in the interspike interval depends on the properties of the stimulus
presented to an animal [de Ruyter van Steveninck et al., 1997] . The
response properties of the neurons to static stimuli were highly variable
between stimulus presentations. The variance in interspike intervals between
stimulus presentations was essentially proportional to the mean firing
rate, suggesting that the variation was Poisson distributed . In contrast,
when the stimuli were more dynamic and " natural " the responseof the HI
122
4. Encoding
in Neuronal Activity
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Figure 4.7. Variability of interspikeintervalsin a corticalneuronwith constantor
fluctuatingcurrent. (A ) Superimposedrecordingsof a regular-firing layer5 neuron,
from 10consecutivetrials with a superthresholdd.c. current pulse (middle), also
shown as a rasterplot with 25 consecutivetrials (lower). (B) The sameas in (A )
but the stimuluswasa repeatedsignalfluctuatingwith Gaussiandistributedwhite
noise. From[Mainenand Sejnowski
, 1995].
neuron to a particular signal was highly reproducible . An analysis of the
information carried in the spike train showed that approximately half of
the variation was signal and the other half was noise. The information rate
was approximately 2. 5 bits in 30 milliseconds (seealso Section 1.1.3.4).
[Mainen and Sejnowski, 1995] have shown in an in vitro study that neurons
in the visual cortex are capable of remark ably precise action potential
timing . Their results suggest that the variability found in vivo is a result
of variation in the incoming synaptic barrages from one stimulus presentation
to the next. The neurons fired with a much higher temporal consistency
in response to a repeated randomly fluctuating signal than to a
fixed d.c. current pulse . The fluctuating signal was constructed by adding
filtered white noise generated by a computer to a constant depolarizing
pulse . An example of the data from this experiment is shown in Figure 4.7.
The spike trains produced by the fluctuating input were reproducible to
less than one millisecond .
In a recent experiment , Nowak and coworkers took this analysis a step further
[Nowak et al., 1997] . They recorded from three different types of cells
in the visual cortex of a ferret (in vitro ). When presented with a fixed level
current offset these cells are have different characteristic firing patterns, including
: regular spiking, fast spiking and bursting . In contrast when presented
"
"
with activity recorded from previously described chattering cells
[Gray and McCormick , 1996], all of the cell types had similar firing pat -
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4.6 Interspike Interval Variability
123
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Figure 4.8. Response of one cell in area Mf in a behaving macaque monkey to
the two second presentation of a random dot pattern . Each raster pattern in the
panel on the left shows the response of the cell to a different random dot pattern .
The panel on the right shows the response to multiple presentations of the same
random dot pattern, which were interleaved with other stimuli . While the response
patterns in the left hand panel appear to capture only the onset of the stimulus .
It is clear from the right hand pattern that other features of the stimulus pattern
are reliably captured . The lower part of each panel contains a poststimulus time
histogram (seeSection 1.1.2. 2). Reprinted from [ Bair and Koch, 1996] .
terns. They also presented the cells with a range of different noise signals
with different spectral characteristics. When presented with real input the
cells had a more variable firing pattern, but the firing was more consistent
between stimulus presentations. The consistency was present in a much
higher reliability and in less temporal jitter .
A similar result was also found in cells in the medial temporal area ( V5
or MT ) of the awake behaving macaque monkey [Bair and Koch, 1996] .
Evidence sugg,eStsthat this area is involved in visual motion processing
[Dubner and Zeki , 1971] . Bair and Koch examined the activity patterns
of neurons in response to different random stimuli . As shown
in Figure 4.8, when data from different random stimuli were compared
the response could be characterized by a transient followed spikes separated
by a Poisson random set of interspike intervals . This data alone
could be interpreted as evidence for errors or noise in neuronal activity
124
4. EncodingInformationin NeuronalActivity
[Shadlen and Newsome, 1994] . However when presented multiple times
with the same random stimulus (right panel of Figure 4.8) there was a high
degree of consistency in the firing pattern of the neuron and very little jitter
.
Most recently Buracas and coworkers [Buracas et al., 1997] used a Gabor
function pattern moved in two or eight directions to study firing patterns
of neurons in area MT of behaving macaque monkeys. They measured
the information provided by the spike train n response to a stimulus that
moved uniformly to one which randomly reversed direction every 30 to
300 ms. The primary finding in this study was that the neurons produced
approximately 1 bit of information per second with a constant speed stimulus
, and as many as 29 bits per second in responseto dynamically changing
stimulus .
The results were consistent with the findings of Bair and Koch in that the
neurons fired with a reliable sequence in response pattern to a repeated
random stimulus , but with highly variable spike trains in response to different
random stimuli . They suggest that a neuron codes for the stimulus
that results in the highest information rate, rather than the stimulus that
produces the highest firing rate.
Buracas and coworkers also measured the information rate as a function
of the time after the start of the constant stimulus pattern .
Consistent with prior findings of in primate inferior temporal cortex
[Optican and Richmond , 1987, Tovee et al., 1993] most of the information
is in the first few hundred milliseconds after the onset of the stimulus pattern
.
Recent experimental evidence suggests that more realistic stimuli and dynamic
stimuli that place more demands on the processing of information
within a system of neurons result in reliable and more variable firing patterns
of the neurons.
4.7 Synapses and Rate Coding
Some of the strongest evidence against a simple rate code has come from
recent studies of the nature of synaptic transmission between pyramidal
cells in layer 5 of the rat visual cortex [Markram , 1997] . Paired activation
in these synapses, as in other brain regions, has been shown to increasethe
influence of the presynaptic cell on the activity of the postsynaptic cell in a
manner initially suggestedby [Hebb, 1949] . However the properties of the
synapsesboth before and after this change are not ideal for the use of rate
coding .
As illustrated in Figure 4.8, [Markram and Tsodyks, 1996] demonstrated
that modification of the synapse does not result in an increase in synaptic
efficacy at all frequencies. With the frequency of input spikes shown
in the figure , the response to the initial presynaptic action potential is p0tentiated , but the response to the subsequent action potentials is attenuated
. The top trace contains the average excitatory post-synaptic potential
EPSP
) before (solid line ) and after (dashed line ) pairing activity in the two
(
pyramidal cells, measured as a result of the stimulation sequenceshown in
I;.
.~ --.
.
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.
vm
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im
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.
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4.8 Summary and Implications
125
Figure 4.9. Effect of paired activation of synaptically .connectedlayer V tufted cortical
cells. The top panel shows the average EPSP before (solid line ) and after
line ) paired activation . The center panel shows the integral of the nor dashed
(
malized EPSPs, and the lower panel shows the presynaptic stimulation . Modified
from [Markram, 1997] .
the bottom trace. The center part of the figure contains the integral of the
EPSPdata shown in the top part of the figure . Note that one effect of the
potentiation of the initial input and depression of later inputs is to increase
the synchrony in the activity of the pre and post synaptic cells.
In later studies [Tsodyks and Markram , 1997, Abbott et al., 1997] it was
shown that the post-transient effective synaptic strength is inversely proportional
to the firing rate of the presynaptic neuron . This effectively cancels
the persistent firing rate signal in the postsynaptic neuron, but leaves
a strong response to a transient change in firing rate. These new insights
into the synaptic modification rules suggest that some synapsesdo not effprt1vp1vtr ~n~mit nPT~i~tpnt T~tp rndp infnTm~tinn - Thi ~ i~~tIP win hP di ~
4.8 Summary and Implications
In this chapter, a small number of selected examples have been presented
to illustrate the ways in which the rate coding hypothesis is being changed.
126
4. EncodingInformationin NeuronalActivity
Recent data on the temporal structure of the activity of neurons and the
properties of synaptic transmission have highlighted a need to use more
realistic computational models to study the properties of systems of neurons
. Highlighted differences in the reliability of neuronal firing that result
when comparing stimulation with artificial and with more realistic inputs
. In particular fixed firing rates and fixed synaptic weights will most
likely be insufficient to model the properties of real neurons. The spiking
neuron models described in the other chapters of this book capture some
of the essential structure needed to construct useful models of systems of
neurons. The importance of explicitly modeling the temporal structure of
neuronal activity has been made elsewhere [Gerstner et al., 1993], and they
have demonstrated that an associative memory can be constructed with
spiking neurons.
It is clear that firing rate coding is used by neurons to signal information .
However the temporal structure of this firing rate code is likely to contain
additional information, which may only be used by a subset of the downstream
neurons that receive the message. These examples also highlight
the importance in simultaneously measuring the activity patterns in large
numbers of neurons and the temporal interactions between these neurons.
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Part II
Intplententations